now we are looking for a line x=a'y + a'b
We need to run two LPs - one for when the gradient is positive and one for when it's negative, looking for the max or min value of a' (and lateer substituting a=1/a'.)
our constraints are that for every segment $x_1 \leq a'y-a'b$ and $x_2 \geq a'y-a'b$